1. Field of the Invention
The present invention relates to generating signals in a telecommunication system, and, more particularly, to generating complex Rayleigh fading signals.
2. Description of the Related Art
Fading of a transmitted signal is a characteristic of an over-air channel of, for example, wireless, cellular, and radio telecommunication systems. Fading causes distortion of the transmitted signal with variations in signal amplitude and phase. Distortion of the transmitted signal degrades the operation of a receiver that reconstructs the data contained in the transmitted signal, affecting the reliability and quality of the communication link. Design of robust wireless or similar systems may focus on methods to reduce the effects of fading. Generating fading signals allows for simulation of the transmission channel and allows for development, performance testing, and verification of designs without extensive testing of the design in the actual field environment. Such testing is both expensive and time consuming, especially when many different design aspects are considered.
Complex Rayleigh fading signals are commonly employed for simulation and may be generated in accordance with the Jakes fading model. The in-phase (I) and quadrature-phase (Q) (fading signal) components rI(t) and rQ(t) in accordance with the Jakes fading model of the prior art are as given in equations (1) and (2). The gain parameters of equations (1) and (2) are defined in equation (3):                                           r            I                    ⁡                      (            t            )                          =                                            2                        ⁢            cos            ⁢                          xe2x80x83                        ⁢            αcos            ⁢                          xe2x80x83                        ⁢                          ω              m                        ⁢            t                    +                      2            ⁢                                          ∑                                  n                  =                  1                                M                            ⁢                              cos                ⁢                                  xe2x80x83                                ⁢                                  β                  n                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                                  ω                  n                                ⁢                t                                                                        (        1        )                                                      r            Q                    ⁡                      (            t            )                          =                                            2                        ⁢            sin            ⁢                          xe2x80x83                        ⁢            α            ⁢                          xe2x80x83                        ⁢            cos            ⁢                          xe2x80x83                        ⁢                          ω              m                        ⁢            t                    +                      2            ⁢                                          ∑                                  n                  =                  1                                M                            ⁢                              sin                ⁢                                  xe2x80x83                                ⁢                                  β                  n                                ⁢                cos                ⁢                                  xe2x80x83                                ⁢                                  ω                  n                                ⁢                t                                                                        (        2        )                                                      ω            n                    =                                    ω              m                        ⁢            cos            ⁢                          xe2x80x83                        ⁢                                          n                ⁢                                  xe2x80x83                                ⁢                π                                                              2                  ⁢                  M                                +                1                                                    ,                  xe2x80x83                ⁢                              β            n                    =                                    n              ⁢                              xe2x80x83                            ⁢              π                                      M              +              1                                      ,                  xe2x80x83                ⁢                  1          ≤          n          ≤          M                                    (        3        )            
where xcfx89m is the fading bandwidth and xcex1 is a constant generally set to zero, but may take on other values for particular implementations to adjust for system and/or transmission channel characteristics.
A system of the prior art for generating complex Rayleigh fading signal components rI(t) and rQ(t) according to the Jakes fading model is shown in FIG. 1. The system 100 includes M pairs of in-phase (I) and quadrature-phase (Q) paths 110(1)-100(M) and 111(1)-111(M), respectively (M an integer and 1xe2x89xa6nxe2x89xa6M). The nth pair of I and Q paths 110(n) and 111(n) includes a corresponding signal generator 101(n) generating a signal with frequency xcfx89n. Each of the I and Q paths 110(n) and 111(n) for the nth path pair has gain adjustment of the corresponding signal by amplifiers 102(n) and 103(n), respectively. The gain parameters for the adjustment are determined as given in equation (3). An additional path pair 106 and 114 of I and Q paths includes a corresponding signal generator 107 generating a signal with frequency xcfx89m, and this frequency is either based on or equivalent to the fading bandwidth. Each of the I and Q paths 106 and 114 for the additional path pair has gain adjustment by amplifiers 108 and 109, respectively, with gain parameters determined as given in equation (3).
The output signals of the amplifiers 102 and 108 for all I paths are summed in adder 113 to provide the I component rI(t) of fading signal r(t). The output signals of the amplifiers 103 and 109 for all Q paths are summed in adder 112 to provide the Q component rQ(t). Adders 112 and 113 may not necessarily be employed if the addition of signals is within the transmission channel.
The advantages of generators that employ the Jakes fading model are (i) the implementation of the generator is relatively simple; (ii) some of the statistical quantities of the model generally agree with or closely approximate the characteristics of ideal channel fading; and (iii) implementations may simultaneously generate multiple fading signals uncorrelated with one another. The Jakes fading model, however, deviates from the ideal fading significantly in that the Jakes model autocorrelation values for the in-phase and quadrature components are different from one another, while the two autocorrelation values for the in-phase and quadrature components for ideal fading signals are generally equivalent.
The autocorrelation values xcfx86rI(t) and xcfx86rQ(t) for the I and Q components rI(t) and rQ(t), respectively, are given in equations (4) and (5).                                           φ            rI                    ⁡                      (            t            )                          =                                            lim                              T                →                ∞                                      ⁢                                          ∫                0                T                            ⁢                                                                    r                    I                                    ⁡                                      (                                          τ                      +                      t                                        )                                                  ⁢                                                      r                    I                                    ⁡                                      (                    τ                    )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  τ                                                              =                                                    cos                2                            ⁢              αcos              ⁢                              xe2x80x83                            ⁢                              ω                m                            ⁢              t                        +                          2              ⁢                                                ∑                                      n                    =                    1                                    M                                ⁢                                                      cos                    2                                    ⁢                                      β                    n                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      ω                    n                                    ⁢                  t                                                                                        (        4        )                                                      φ            rQ                    ⁡                      (            t            )                          =                                            lim                              T                →                ∞                                      ⁢                                          ∫                0                T                            ⁢                                                                    r                    Q                                    ⁡                                      (                                          τ                      +                      t                                        )                                                  ⁢                                                      r                    Q                                    ⁡                                      (                    τ                    )                                                  ⁢                                  xe2x80x83                                ⁢                                  ⅆ                  τ                                                              =                                                    sin                2                            ⁢              αcos              ⁢                              xe2x80x83                            ⁢                              ω                m                            ⁢              t                        +                          2              ⁢                                                ∑                                      n                    =                    1                                    M                                ⁢                                                      sin                    2                                    ⁢                                      β                    n                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      ω                    n                                    ⁢                  t                                                                                        (        5        )            
As given by equations (4) and (5), xcfx86rI(t) is not equivalent to xcfx86rQ(t) unless sin2xcex2n=cos2xcex2n for n=1, . . . , M and sin2xcex1=cos2xcex1. However, for the condition that xcfx86rI(t) is equivalent to xcfx86rQ(t), rI(t) must be equivalent to rQ(t), (i.e., the fading signal has identical real and imaginary parts). For the ideal fading model, the real and imaginary components of the fading signal are desirably independent, and so these conditions are not desirable for a complex fading signal generator.
The present invention relates to generating one or more complex fading signals. A fading signal may be generated by generating in-phase (I) and quadrature phase (Q) signals for each of a plurality of complex carriers, each complex carrier having a frequency related to a fading bandwidth of the complex fading signal; and providing i) one or more of the I signals corresponding to an I component of the complex fading signal, and ii) one or more of the Q signals corresponding to a Q component of the complex fading signal. For each fading signal, the I and Q components of the complex fading signal have substantially equivalent autocorrelation values.